Lie Point Symmetries for Reduced Ermakov Systems
arXiv:nlin/0404031 · doi:10.1016/j.physleta.2004.08.051
Abstract
Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2,R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of motion of an ion under a generalized Paul trap.
References in corpus (10)
- The Ermakov-Pinney Equation in Scalar Field Cosmologies
- Cosmic Dynamics of Bose-Einstein Condensates
- Time-Dependent Hilbert Spaces, Geometric Phases, and General Covariance in Quantum Mechanics
- Dynamical symmetries and the Ermakov invariant
- Anisotropic Bose-Einstein condensates and completely integrable dynamical systems
- On the Lie symmetries of a class of generalized Ermakov systems
- On the linearization of the generalized Ermakov systems
- Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation
- Gravitational bouncing of a quantum ball: Room for Airy's function Bi
- On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group